Should I make my model into 1 whole or multiple parts?
I would say model all separate objects as separate meshes and group all objects that form a single continuous surface.

In the case of the human model it should probably be a single mesh object, since it is a "continuous single skin surface", that way you won't get discontinuities, artifacts or seams while rendering. 

Edit: I am not into character modeling so my view here is bound to be inaccurate, as suggested below, a clothed character can optimally be subdivided into the several visible patches of skin, like say head, hands, legs, etc. 

As for the background scene divide it sensibly as much as possible.
Take advantage of cloning and instances whenever possible for scene optimization. It can save a lot in file size, memory management while rendering and a lot of manual work updating different objects.
Terrain can be one single big mesh, each individual tree and vegetation should be single objects, etc.